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A number of finite element modeling approaches for reinforced concrete (RC) structural walls have recently become available for both research purposes and design applications. Five conceptually-different state-of-the-art finite element models for RC walls are described and evaluated in this paper, including models based on either a fixed-crack or a rotating-crack approach for simulating the biaxial behavior of concrete under plane-stress state, models characterized with either a single- or a multi-layered representation of the wall cross-section, and models with or without consideration of various individual failure mechanisms (e.g., buckling of reinforcement, out-of-plane instability). Modeling approaches were validated against experimental data obtained for five benchmark RC wall specimens, all with rectangular cross-sections, yet are differentiated by a range of salient response characteristics (e.g., aspect ratio, axial load, failure mechanism), in order to assess the capabilities of the models in representing the response of isolated planar walls under uni-directional lateral loading, as well as to identify future research directions. Results presented suggest that the models considered in this study can all capture the lateral load at yield and the peak lateral load capacity of the wall specimens with ±10% accuracy, while the initial stiffness and yield stiffness can be overestimated as much as 3.0 and 1.8 times, respectively. All models can capture nonlinear shear deformations and interaction between flexural and shear responses under cyclic loading, where the analytically-predicted flexural and shear deformations are within ±30% of the experimentally-measured values. Moderate differences between the predicted crack orientations and distributions are noted between the models, and the model results for the magnitudes of principal compressive stresses in concrete and the extent of stress localization are comparable. All models can capture the nonlinear distribution of vertical strains measured along the base of the walls, where the magnitudes of the predicted tensile and compressive strains are within ±50% of experimentally-measured strains for most models. Although some of the model formulations proved to be successful in capturing the experimentally-observed strength loss mechanisms for individual wall specimens, none of the models were capable of comprehensively simulating all of the strength degradation mechanisms observed during the tests.

After the 2010 Maule, Chile, earthquake (Mw 8.8), several reinforced concrete (RC) buildings presented damage in some walls (crushing of concrete, buckling and fracture of steel reinforcement). These buildings had been designed according to the up-to-date seismic standards in the country and were not expected to suffer damage as severe as what was observed. Common features of the damaged walls were: little or no confinement at the wall ends; relatively high axial load; narrow thicknesses (below 200 mm); and discontinuities in height. Slender RC walls are often used in Chile and commonly, due to architectural constraints, the length of the walls changes between floors designated for parking use and the upper floors, creating a setback in the lower levels. These types of walls are commonly called “flag walls”. The problem of discontinuity has not been investigated experimentally and therefore it is necessary to observe its impact in RC walls. Four structural wall specimens were designed, one with no discontinuity and the other three with different sizes of the setback. They were tested under a nominal constant axial load of 0.1f'cAg and cyclic lateral loads increasing at specific drift levels. Conventional instrumentation and photogrammetry were used to monitor the tests. The experimental results show that the impact of the setback, for the sizes tested, is not significant for the strength but it is relevant for the strength degradation and deformation capacity. Strains in the extreme fibers, curvature and principal strains are studied using photogrammetry. It is found that the plastic hinge length increases with drift, but it remains constrained to the setback region. Another discontinuity is found around the reinforcement of the setback where large concentration of strains can cause premature failure of the wall.

According to Chilean design practice, walls usually have complex geometries and discontinuities in height, mainly in the first story. However, the Chilean design code, similar to many design codes, does not provide special provisions for discontinuities. This paper shows the results of an experimental and numerical study of walls with a central opening at the base. Four slender walls are constructed with the same general dimensions, but with different shapes of the opening (15% and 30% of the length, and 11% and 22% of the wall height). The specimens were tested under constant axial load, while cyclic lateral loading is applied at the top. One of the specimens presents slab elements at the base. Results indicate that lateral strength is similar in all cases; however, displacement capacity varies with opening size. All specimens with openings have less ductility, where the specimen with wider and taller opening had a reduced displacement capacity (∼30% reduction). The width of the opening was more influential than the height in the displacement capacity. Numerical analysis was done through a finite element modeling, where one of the models considered all features of the formulation and a second model considered rigid beams placed in all levels forcing the Bernoulli hypothesis (flexural model). Both models can capture strength, stiffness and displacement capacity, and therefore a flexural model can be used for boundary detailing.

A model capable of predicting the shear response of beam-column joints subjected to seismic actions is presented. The analytical model, originally developed for walls and based on a simple physical formulation, is adapted. It considers mean stress and strain fields based on a reinforced concrete panel representing the joint, under the assumption that the principal concrete stress and principal strain directions coincide. Simple constitutive material laws are considered for concrete and steel. To estimate the shear capacity, the model satisfies the equilibrium in the longitudinal (vertical) direction. In order to analyze the accuracy of the model, a database integrated by 92 tests of exterior and interior beam-column joints is collected from the literature. Noting that the original model does not consider the effect of confinement product of adjacent elements to the connection, this effect is introduced through factors that reduce the values of the longitudinal and transverse strain used to calibrate the angle of the strut. In addition, the contribution of the transverse reinforcement in the capacity of the element is included. These modifications together with the influence of the boundary reinforcement, yields a good strength estimate for exterior and interior joints that fail in shear. When comparing with other models from the literature, it is observed that the proposed model provides one of the best correlations.

The capacity of structural systems subjected to shear loads commonly distinguished by discontinuities such as point loads or supports, or abrupt changes of cross section, where complex fields of stresses and strains are generated, is vital information for design. Four structural systems that present stress concentration due to applied shear loads are commonly short walls, deep beams, corbels and beam-column joints. In the present work a model is developed to predict the shear capacity of these elements based on a panel model that considers average strain and stresses in a reinforced concrete orthotropic material, which covers the section of the structural element subjected to stress concentration. In addition, the panel element complies with the longitudinal equilibrium, by equalizing the applied axial load with the internal stresses of the structural element, requiring constitutive material laws for both concrete and steel reinforcement. The original model that has shown good shear strength prediction requires solving the non-linear equation of vertical equilibrium. Thus, this work eliminates the need to solve the iterative problem for the capacity estimation of four possible limit states (failure of concrete in tension and compression, and yielding of longitudinal web and boundary reinforcement). For that, an expression is calibrated for the strain of the model with respect to relevant parameters, for each limit state, that allow the generation of a non-iterative model. The model results in an average predicted capacity over experimental capacity ratio, V model / V test , of 1.0 and a COV of 0.25, with similar performance for all four structural systems. When comparing these results with the general model that requires an iterative method, a similar performance is observed, with an average strength ratio and COV of 0.98 and 0.23, respectively. Likewise, in comparison with the ACI 318, the latter shows worse predictions (on average 24% lower) and with greater scatter (on average 28% higher). The expression in AASHTO code presents better correlation than ACI with predictions closer the proposed model.

The level of existing research, as well as current code provisions and modeling approaches, are not adequate to characterize the behavior of squat reinforced concrete walls with shear – controlled responses. In this study, an experimental program was conducted to investigate the shear-dominated response attributes of eleven squat wall specimens; including their failure mode, lateral load capacity, ductility, hysteretic response characteristics, and deformation characteristics. Test parameters included the wall aspect ratio, the amounts of vertical and horizontal web reinforcement and longitudinal boundary reinforcement, and the level of axial load. The experimental findings are presented and discussed in this paper, with emphasis on the observed failure mode, shear strength, deformation capacity, and strength degradation characteristics of the walls tested, as well as the contribution of shear, flexural, and sliding deformations to wall lateral displacements. Comparison of the test results with backbone curves specified in performance assessment guidelines is also provided.

A research was conducted to develop a macroscopic modeling approach that integrates axial, flexure, and shear interaction under cyclic loading conditions to obtain reliable predictions of the nonlinear response of reinforced concrete (RC) structural walls. The model, named as Efficient-Shear-Flexure-Interaction (E-SFI), is intended to provide accurate results for squat, medium-rise, and slender planar walls, with a computationally efficient formulation that can be used under generalized conditions. The E-SFI model, which is based on the Shear-Flexure Interaction Multiple-Vertical-Line-Element-Model (SFI-MVLEM), incorporates a two-dimensional RC panel behavior described with a fixed-crack-angle approach. The novel formulation removes the internal degree of freedom per RC panel element of the SFI-MVLEM by incorporating a calibrated expression to compute the horizontal normal strain ( e x ), and therefore removing the assumption of zero resultant horizontal stress ( σ x = 0 ) to increase the range of applicability of the model. Three RC wall specimen tests were selected to calibrate and validate the E-SFI model, as well as to prove the model efficiency, including a slender wall (shear span-to-depth ratio of 3.0), a medium-rise wall (shear span-to-depth ratio of 1.5), and a squat wall (shear span-to-depth ratio of 0.63). Analytical model results reveal the ability of the model to accurately reproduce the hysteretic response for all considered cases, with an important reduction in the runtime and an improved current tangent convergence rate compared with the SFI-MVLEM.

In shear wall building design, the initial process requires the interaction between the architectural and structural engineering groups to define the adequate wall layout, usually done with a trial-and-error procedure to fulfill architectural and engineering needs, slowing down the design process. For the engineering analysis, first, the wall thickness and length are required to check the building deformation limits, base shear strength, among other parameters. For this reason, the present investigation develops a structural design platform for reinforced concrete wall buildings that uses a deep neural network to predict the wall’s thickness and length based on previous architectural and engineering projects. The study includes, in the first place, the surveying of the architectural and engineering plans for a total of 165 buildings constructed in Chile; the generated database has the geometric and topological definition of the walls and the slabs. As a second stage, a model was trained for the regression of the wall segments’ thickness and length, making use of a feature vector that models the variation between the architectural and the engineering plans for a set of conditions such as the thickness, connectivity (vertical and horizontal), area, wall density, the distance between elements, wall angles, foundation soil type, among other engineering parameters. The regression model results in terms of R2-value are 0.995 and 0.994 for the predicted wall thickness and length, respectively, proving to be a reliable method for the initial engineering wall definition.

In the structural design of shear wall buildings, the initial process requires the interaction between the architecture and engineering teams to define the appropriate distribution of the walls, a stage typically carried out through a trial-and-error procedure, without any consideration of previous similar projects. In previous work, a database of 165 Chilean residential projects of reinforced shear wall concrete buildings was built, which fed a regressive neural network model to predict the wall’s engineering thickness and length values from an architectural 30-feature input vector, which accounts for geometric and topological properties, archiving remarkable results regarding the coefficient of determination ( R 2 ). However, a regressive model of this nature does not incorporate a spatial detail or contextual information of each wall’s perimeter, and also, the prediction of other parameters such as the wall translation has a poor performance. For this reason, the present research proposes a framework based on convolutional neural network (CNN) models to generate the final engineering floor plan by combining two independent floor plan predictions, considering the architectural data as input. The first plan prediction is assembled using two regressive models that predict the wall engineering values of the thickness, the length, the wall translation on both axes from the architectural plan, and the floor bounding box width and aspect ratio. The second plan prediction is assembled using a model that generates a likely image of each wall’s engineering floor plan. Both independently predicted plans are combined to lead the final engineering floor plan, which allows predicting the wall’s rectangles design parameters and propose new structural elements not present in architecture, making the methodology an excellent candidate to accelerate the building wall layout’s early conceptual design.

In this article, the sectional behavior (strain and stress) and the effective width in T-shaped reinforced concrete wall are analytically studied. For the parametric study, a nonlinear quadrilateral thin flat layered shell element with 6 degrees of freedom (DOF) per node for the modeling of reinforced concrete wall structures developed by Rojas et al. (2019) is used, varying the axial load (AL), longitudinal steel ratio of the web (LSRW) and flange (LSRF) boundary, aspect ratio (AR) relative to the length of the web of the wall (lw) and height of the wall (hw), and length of the flange (Lf). The parametric study is used to compare the element response that couple the axial, flexion and shear behavior, with a model that only incorporates the coupling of flexion and axial, maintaining plane sections (flexural model). Based on the parametric study, it is calibrated an analytic model of the strain profile of the tension flange of T-shaped walls. Additionally, by including the effect of shear in the model, amplification of the maximum compression strain and a reduction of the maximum tensile strain in the web is observed, mainly in squat walls. Besides, the parametric study is also used to calculate the effective width of T-shaped walls with the flange in tension, finding that it depends mainly on the length of the flange and the roof drift. After initiation of yielding in the flange, the effective width grows quickly, concluding that independent of the geometry and the slenderness, the effective width of the flange in tension covers the entire section if yielding is expected.

Reinforced concrete structural walls are commonly used to provide lateral strength and stiffness to resist lateral loads from wind or earthquake. Slender walls usually require large amounts of longitudinal reinforcement at wall boundaries to satisfy code lateral strength requirements; therefore, use of structural steel reinforced concrete (SRC) walls, where the boundary longitudinal reinforcement is replaced by a structural steel section, is a potentially attractive alternative. This study presents results of an experimental program involving tests under combined gravity and lateral loading for three, heavily instrumented, moderate-scale SRC slender walls. Primary test variables included varying the size of the embedded structural steel section and the quantity of transverse reinforcement provided at the wall boundaries. Although slip of the structural steel was observed for all specimens, test results reveal good behavior up to and beyond 2% lateral drift, even for a specimen with only modest confinement at the wall boundaries.

In this article, the formulation and verification of a nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the nonlinear analysis of reinforced concrete (RC) walls under static and cycling loads are presented. The formulation is based on a quadrilateral element with twelve degrees of freedom (DOF), two displacements and one drilling DOF per node, which is defined by a blended field interpolation for the displacements over the element, and a layered system for the element section consisting of fully bonded, smeared steel reinforcement and smeared orthotropic concrete material with a rotating angle formulation, and a stiffness tangent approach. The drilling DOF refers to the incorporation of the in-plane rotation as a DOF at each element node. The blended field interpolation has the advantage of producing a smoother strain distribution inside each element, which facilitates element convergence, and the layered section formulation allows for the properties of the concrete and steel over the thickness of the wall to be modified to properly represent the different wall components, such as the concrete cover, steel rebar and confined concrete. Additionally, the formulation introduces a rotational DOF at each node, which allows the membranes to connect directly to beam and column elements. Moreover, this formulation incorporates the coupling of axial, flexural and shear behavior observed on the different configurations of RC wall structures. To verify this formulation, the results of a set of available experimental data reported in the literature for RC wall elements, with different configurations (slender walls, squat walls, wall with irregular disposition of openings) and levels of confinement, under monotonic and reversed loads are compared with the results obtained from the corresponding analytical model. The formulation is notably consistent with the experimental data and can predict the maximum capacity, the global (force vs deformation) and local responses (strain along the wall) and incorporate the coupling of axial, flexural and shear behavior observed in the different configurations of RC wall structures.

Dynamic shear amplification has been commonly studied in cantilever reinforced concrete wall systems, however, coupling beams or slabs can generate axial loads that can modify the response. A parametric study is carried out that covers 432 nonlinear time-history analyses (72 models with 6 records) of 2 coupled walls with different length, including variations in the amount of boundary element steel ratio (1%, 3% and 5%), amount of slab steel ratio (0.0%, 0.3% and 0.6% − 0.0% is defined for connected walls without coupling), building height (25 m, 50 m and 75 m), and wall length (2 m, 4 m and 6 m). The walls are represented with nonlinear fiber models; while the coupling slabs are elastic within the length with a rigid-perfectly plastic model at both element ends. The shear amplification values depend on the coupling level, with the highest amplification values ​​being observed for connected (not coupled) systems. The high values ​​for connected walls are due to the rapid plastification of the wall because of the low structural redundancy. The mean shear amplification values are 1.45, 1.10 and 1.35 for coupling slabs with reinforcing steel ratio of 0.0%, 0.3% and 0.6%, respectively. The proposed expression for the dynamic shear amplification also depends on the response modification factor of the walls, a parameter directly related to nonlinearity sources. On the other hand, an expression used by many codes that depends on the number of floors does not necessarily represent the amplification that occurs in tall buildings with moderate coupling, since the plastification at the base in such cases is difficult to achieve given their large elastic displacement capacity, as well as, cases that incorporate a minimum base shear criterion, that reduce the nonlinearity incursions.

Columns that are at the intersection of frames in two different directions are subjected to biaxial shear when lateral loads are simultaneously applied in two directions. Using the resultant shear and evaluating one-way shear strength along the direction of the resultant force, as most design codes do, is unconservative especially when significant shear co-exist about both axes. The conservatism of one-way shear strength in some expressions of ACI 318 (14) balances the not consideration of biaxial shear design in the code. However, the use of more refined or accurate expressions as in ACI 318 (19) makes the consideration of biaxial shear for design a need. Experimental data from the literature is used to compare ACI 318 expressions and validate the trilinear interaction diagram approach included in ACI 318 (19) for biaxial shear loading, showing that it is a simple and reliable method for design.

Masonry walls are structural elements generally used in housing or small buildings. Given their structural configuration, they commonly present shear failure due to seismic actions, characterized by a fragile response. Thus, it is important to have simple, yet reliable tools that correctly estimate the shear capacity of walls. For that, a simple existing model developed for reinforced concrete elements and based on a panel model is used and adapted to masonry walls, providing a novel formulation that can be applicable to both materials. For compression and tension behavior, the prismatic resistance of the panel is used, which, due to the anisotropy of the material, degrades with the angle formed by the load with the vertical mortar joint. Strain values are set for compression and tension failure modes, and a degradation coefficient in compression due to the biaxial strain loading is included. Additionally, bond failure is also incorporated into the model. A database of 41 tests of reinforced masonry walls and 12 tests of confined masonry walls is used for model validation. The strength ratio between the shear strength obtained by the model and the test is compared, giving an average and a coefficient of variation (COV) of 1.0 and 0.15, respectively for reinforced walls, and 1.08 and 0.14 for confined walls, showing a satisfactory performance and better behavior than simple models from the literature. The analysis of general trends of the strength ratio reveals that there is a low dependence between the strength ratio and the studied parameters, implying that the model captures the physical behavior of masonry walls.

Buckling of longitudinal reinforcement in reinforced concrete (RC) columns or walls is commonly seen with a length equal to the spacing between stirrups (local buckling), but experimental observations have shown that the length of buckling can span a larger length, deforming several stirrups within the buckling length (global buckling). The behavior of the longitudinal reinforcement under compression resulting in global buckling is studied in this work, based on a concentrated plasticity fiber model that considers four (4) plastic hinges. The model was originally validated for local buckling and here is extended to global buckling by introducing the effect of transversal reinforcement and expansion of the core concrete in the analysis. Modeling of the forces from the stirrups acting on the longitudinal bar assumes that part of the force is transferred directly to the expanding concrete core and the remaining force is balanced by internal stresses in the longitudinal bar. The bar buckling behavior is evaluated for different buckling length values and the length is chosen such that it delivers the lowest maximum stress. The proposed model is validated by comparison of the predicted buckling mode with experimental test results from the literature. The average error in the mode prediction is −0.59 (about half the space between stirrups), which is a reasonably good value considering that the database of tests used covers buckling modes from 1 to 7 (stirrup spacing). Besides of providing good critical buckling length predictions, it allows obtaining the stress versus strain curve for the overall buckling bar. Analysis of three column specimens from the literature indicates that the overall stress versus strain response can be obtained with a reasonable accuracy. Peak stress is obtained within an error of about 10% compared to the test result for a strain well represented by the model. The post-peak slope also gives a good estimate for the degradation stage.

This work validated a model of shear–flexure interaction for prestressed self-consolidating concrete beams with varied shear span-to-depth ratios, which were tested under four-point bending as part of this work. The interaction between flexure and shear was introduced by a panel element’s biaxial behavior in a modified fiber element formulation. Two different assumptions were considered for the interaction model implementation: (i) zero transverse normal stress perpendicular to the beam axis in any cross section, and (ii) a prescribed transverse normal strain profile along the beam based on the model calibrated for cantilever members. The interaction model with a prescribed transverse strain profile and with a consideration of flexure-induced deformations had better predictions of capacity and deformation for the tested beams, as well as the transverse normal strain profile, compared to the other models.

The Mw 8.8 earthquake in 2010 in Chile provided valuable information regarding the damage and potential design code changes for reinforced concrete (RC) structures. Many modern RC buildings suffered severe damage, mainly in the form of concrete cover spalling, followed by longitudinal boundary bar buckling and concrete crushing. The absence of wall boundary detailing explains such behavior, but older structures and thousands of other buildings suffered minor or no damage at all. An analysis of some potential factors that influenced the damage caused is carried out and the fundamental principles for the Chilean RC design code changes are exposed. Currently, a displacement-based approach is used for detailing of the wall boundary elements as well as for establishing damage limitation. Compressive concrete strain cannot exceed 0.008, limiting indirectly the axial load, which is one of the potential precursors of the damage. Transversal reinforcement is also provided in zones of potential yielding of the longitudinal reinforcement such that buckling due to compression preceded by tension is minimized; this buckling is more likely in asymmetric cross-sections, such as T-shaped sections, where usually the web goes into larger tensile and compressive strains given the variation of location of the neutral axis for the web under tension or compression.

Financial support for this project provided by Chile's National Commission on Scientific and Technological Research (CONICYT) for the project Fondecyt 2008, Initiation into Research Funding Competition, under Grant No. 11080010, is gratefully acknowledged.

Reinforced concrete columns in seismic zones are subjected to combined actions, resulting in axial loads in longitudinal reinforcing bars. Thus, knowing the bar’s response, especially when it is subjected to important axial compressive forces that might lead to buckling, is important. A bar buckling model based on concentrated plasticity and with the capability of introducing an initial imperfection is described. The initial imperfection is imposed by bending the bar with a transversely applied nonpermanent force. Additionally, a comprehensive study of the monotonic tensile response beyond the peak stress point and a simple cyclic rule, complete the physical approach of the model. Comparisons of the model with experimental results reveal that peak capacity (average axial stress) is well captured, as well as the post-peak response shape (average axial stress versus strain), with differences observed basically in the peak capacity for specimens with high bar imperfection-to-diameter ratio, and in the shape of the post-peak response for specimens with low bar length-to-diameter ratio.